Understanding Charge Dynamics in Dense Electronic Manifolds in Complex Environments

Photoinduced charge transfer (CT) excited states and their relaxation mechanisms can be highly interdependent on the environment effects and the consequent changes in the electronic density. Providing a molecular interpretation of the ultrafast (subpicosecond) interplay between initial photoexcited states in such dense electronic manifolds in condensed phase is crucial for improving and understanding such phenomena. Real-time time-dependent density functional theory is here the method of choice to observe the charge density, explicitly propagated in an ultrafast time domain, along with all time-dependent properties that can be easily extracted from it. A designed protocol of analysis for real-time electronic dynamics to be applied to time evolving electronic density related properties to characterize both in time and in space CT dynamics in complex systems is here introduced and validated, proposing easy to be read cross-correlation maps. As case studies to test such tools, we present the photoinduced charge-transfer electronic dynamics of 5-benzyluracil, a mimic of nucleic acid/protein interactions, and the metal-to-ligand charge-transfer electronic dynamics in water solution of [Ru(dcbpy)2(NCS)2]4–, dcbpy = (4,4′-dicarboxy-2,2′-bipyridine), or “N34–”, a dye sensitizer for solar cells. Electrostatic and explicit ab initio treatment of solvent molecules have been compared in the latter case, revealing the importance of the accurate modeling of mutual solute–solvent polarization on CT kinetics. We observed that explicit quantum mechanical treatment of solvent slowed down the charge carriers mobilities with respect to the gas-phase. When all water molecules were modeled instead as simpler embedded point charges, the electronic dynamics appeared enhanced, with a reduced hole–electron distance and higher mean velocities due to the close fixed charges and an artificially increased polarization effect. Such analysis tools and the presented case studies can help to unveil the influence of the electronic manifold, as well as of the finite temperature-induced structural distortions and the environment on the ultrafast charge motions.

A spherical box (of 22 Å radius) comprised the N3 4− molecule, treated at a QM B3LYP/SDD/def2-SVP level of theory (already validated for this compound 2 ) and 1462 water molecules at an MM level, described by the TIP3P force field 3 (Fig. S1). The electrostatic interaction between QM and MM layers was treated including the MM charges in the QM Hamiltonian (i.e., an electronic embedding). General AMBER Force Field 4 atom types (and so van der Waals non-bonding parameters) were assigned to the N3 4− system. Non-periodic boundary conditions were introduced as a confining potential to avoid solvent diffusion outside the box. [5][6][7][8] After a 2 ps equilibration step, a ∼ 8.6 ps production run was collected. A T = 298 K temperature was kept through velocity rescaling every 1 ps. The Atom-centered Density Matrix Propagation extended Lagrangian approach (ADMP) was employed: 9,10 the density matrix in an orthonormal Gaussian, atom-centered, basis is propagated along with the nuclear degrees of freedom, avoiding a SCF convergence procedure at each step. A mass-weighting scheme which attributes a higher mass to the core functions was chosen, together with a 0.2 amu bohr 2 valence mass. This allowed to employ a 0.1 fs time step.

Structural results
From the analysis of AIMD in aqueous solution, the N3 4− structure is on average distorted with respect to the symmetric C 2 -like minimum energy geometry in the gas-phase. Vibrational and environmental effects are indeed able to instantaneously lower such symmetry to some extent.
In particular, the isothiocyanate coordination is more bent with respect to the almost linear arrangement of the optimized, gas-phase, symmetric structure (∼ 167 • Ru-N(NCS)-C(NCS) angle). The two axial-equatorial N(dcbpy1)-Ru-N(dcbpy2) angles also slightly deviate from the gas-phase value.
Regarding the cybotactic region, dcbpy oxygen and isothiocyanate sulfur atoms are strongly solvated in water solution, interacting with 3-4 solvent molecules in their first solvation shell. N3 4− structural parameters from gas-phase optimized structure and the selected AIMD frame for RT-TDDFT electronic dynamics are compared to AIMD structural distributions. Values from an optimized gas-phase structure and the snapshot selected for RT-TDDFT electronic dynamics are shown as vertical black and red bars, respectively.
A continuous symmetry measure (CSM) of N3 4− minimal deviation from C 2 symmetry has been evaluated along such trajectory. The index proposed in Refs. 11-13 quantitatively measures the deviation of a structure from its images generated through the symmetry operations of a given point group (C 2 group for N3 4− ), where a resulting lower value in the [0, 1] range corresponds to a more symmetric structure. To improve computational efficiency, a reduced N3 4− model (a smaller model able to retain a symmetry not higher than C 2 as the full N3 4− structure) has been employed for C 2 -CSM calculations. Looking at the distribution from the N3 4− AIMD in water solution (Fig. S4), two small CSM values (∼ 0.1 and 0.2) appear as the most populated, although higher symmetry distortions (∼ 0.45) are occasionally explored. Therefore, compared to the optimized structure (zero CSM value), the dynamical picture offered by the AIMD simulation reveals that N3 4− at room temperature in water solution slightly deviates from the C 2 symmetry, due to vibrational motions and solvent fluctuations (mean C 2 -CSM: 0.21 ± 0.12). In particular, the N3 4− structure from the frame selected for RT-TDDFT electronic dynamics has, in contrast to the optimized, gas-phase, symmetric one, a moderate symmetry distortion (0.13 C 2 -CSM value, Fig. S4), belonging to the first highly-populated peak at ∼ 0.1.   couple of hole-electron orbitals. 14 Moreover, a hole-electron correlation plot from transition density population analysis, calculated with TheoDORE software, 15,16 is provided to further characterize the spatial properties of the CT excitation (Fig. S5). The most stable 5BU conformer (with an orthogonal arrangement of the two rings) has been considered.

Fragment charges cross-correlations
The normalized cross-correlations and corresponding time-delays for each unique pair of group charges from 5BU and N3 4− excited state electronic dynamics are reported.     Mulliken fragment charges with respect to the ground state at the initial state (t = 0) of RT-TDDFT propagation have been compared to the Natural Population Analysis (NPA) ones (Tables S7 and S8).